Thank you for your question. What you described, although it can be charged as Conduct Unbecoming, is fraternization
. But, to answer your questions. These investigations into the actual facts and evidence could be completed in a week or it could be a month or more. It really depends on how many potential witnesses there are and their availability. For example, if a witness is deployed, then it will take time to set up an interview with a local CID agent with that witness and get the information back to the Command who the Officer is attached to.
Once the investigation of the initial evidence is complete, then after that it can take weeks or months to resolve the issue if there is probable cause to believe the misconduct occurred. That is because the Command has to decide if there will be an Article 15
disposition of the charge or charges or whether they want to court-martial the officer. Then if a court-martial, if it is for a General Court-Martial, since that is essentially a felony court, there must be a probable cause hearing (Article 38 hearing--like a grand jury of sorts), and then findings and recommendations, etc. So, that is what might extend the time to resolve the misconduct issue.
Then, after whatever discipline action the Command takes there would likely be a Show Cause Hearing if the Officer was found guilty, where the Officer would be in front of a discharge
board. That process can take a year to resolve. Sometimes less, but it can be lengthy.
Please let me know if you have specific follow up questions as your initial question was a bit broad and without facts. I would be glad to assist you further if I can.